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Updated on: 16 Oct 2018, 01:29
Originally posted by monirjewel on 09 Nov 2010, 01:08.
Last edited by Bunuel on 16 Oct 2018, 01:29, edited 2 times in total.
Last edited by Bunuel on 16 Oct 2018, 01:29, edited 2 times in total.
Renamed the topic and edited the question.
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In the figure above, the area of square region PRTV is 81, and the ratio of the area of square region XSTU to the area of square region PQXW is 1 to 4. What is the length of segment RS?
A. 5
B. 5.5
C. 6
D. 6.5
E. 7
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09 Nov 2010, 01:17
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In the figure above, the area of square region PRTV is 81, and the ratio of the area of square region XSTU to the area of square region PQXW is 1 to 4. What is the length of segment RS?
A. 5
B. 5.5
C. 6
D. 6.5
E. 7
As the area of square region PRTV is 81 then \(RT^2=81\) --> \(RT=9\);
The area of square region \(PQXW=QX^2=RS^2\) and the area of square region \(XSTU=ST^2=(9-RS)^2\);
Given: \(\frac{(9-RS)^2}{RS^2}=\frac{1}{4}\) --> \(\frac{9-RS}{RS}=\frac{1}{2}\) --> \(RS=6\).
Answer: C.
Or: as the ratio of the areas of squares is the square of the ratio of their sides then \(\frac{ST}{RS}=\frac{9-RS}{RS}=\frac{1}{2}\) --> \(RS=6\).
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